This paper describes unsteady flow phenomena of a two-stage transonic axial compressor, especially the flow field in the first stator. The stator blade with highly loaded is likely to cause a flow separation on the hub, so-called hub-corner separation. The flow mechanism of the hub-corner separation in the first stator is investigated in detail using a large-scale detached eddy simulation (DES) conducted for its full-annulus and full-stage with approximately 4.5 hundred million computational cells. The detailed analysis of complicated flow fields in the compressor is supported by data mining techniques. The data mining techniques applied in the present study include vortex identification based on the critical point theory and topological analysis of the limiting streamline pattern. The simulation results show that the flow field in the hub-corner separation is dominated by a tornado-type separation vortex. In the time averaged flow field, the hub-corner separation vortex rolls up from the hub wall, which is generated by the interaction between the mainstream flow, the leakage flow from the front partial clearance and the secondary flow across the blade passage toward the stator blade suction side. The hub-corner separation vortex suffers a vortex breakdown near the mid chord, where the high loss region due to the hub-corner separation expands drastically. In the rear part of the stator passage, a high loss region is migrated radially outward by the induced velocity of the hub-corner separation vortex. The flow field in the stator is influenced by the upstream and downstream rotors, which makes it difficult to understand the unsteady effects. The unsteady flow fields are analyzed by applying the phase-locked ensemble averaging technique. It is found from the phase-locked flow fields that the wake interaction from the upstream rotor has more influence on the stator flow field than the shock wave interaction from the downstream rotor. In the unsteady flow field, a focal-type separation also emerges on the blade suction surface, but it is periodically swept away by the wake passing of the upstream rotor. The separation vortex on the hub wall connects with the one on the blade suction surface, forming an arch-like vortex.

Flow structure and flow loss generation in a transonic axial compressor has been numerically investigated by using a large-scale detached eddy simulation (DES). The data mining techniques, which include a vortex identification based on the critical point theory and a limiting streamline visualization with the line integral convolution (LIC) method, were applied to the DES result in order to analyze the complicated flow field in compressor. The flow loss in unsteady flow field was evaluated by entropy production rate, and the loss mechanism and the loss amount of each flow phenomenon were investigated for the first rotor and the first stator. In the first rotor, a shock-induced separation is caused by the detached shock wave and the passage shock wave. On the hub side, a hub-corner separation occurs due to the secondary flow on the hub surface, and a hub-corner separation vortex is clearly formed. The flow loss is mainly caused by the blade boundary layer and wake, and the loss due to the shock wave is very small, only about 1 percent of the total loss amount in the first rotor. However, the shock/boundary layer interaction causes an additional loss in the blade boundary layer and the wake, which amount reaches to about 30 percent of the total. In the first stator, the hub-corner separation occurs on the suction side. Although only one hub-corner separation vortex is formed in the averaged flow field, the hub-corner separation vortex is generated in multiple pieces and those pieces interfere with each other in an instantaneous flow field. The hub-corner separation generates huge loss over a wide range, however, the loss generation around the hub-corner separation vortex is not so large, and the flow loss is mainly produced in the shear layer between the mainstream region and the separation region. The main factors of loss generation are the boundary layer, wake and hub-corner separation, which account for about 80 percent of the total loss amount in the first stator.

In this study, the hub-corner separation in a multi-stage transonic axial compressor has been investigated using a large-scale detached eddy simulation (DES) with about 4.5 hundred million computational cells. The complicated flow field near the hub wall in a stator with partial tip clearances was analyzed by data mining techniques extracting important flow phenomena from the DES results. The data mining techniques applied in the present study include vortex identification based on the critical point theory and topological data analysis of the limiting streamline pattern visualized by the line integral convolution (LIC) method. It is found from the time-averaged flow field in the first stator that the hub-corner separation vortex formed near the solid part of the stator tip interacts with the leakage flow and secondary flow on the hub wall, resulting in a complicated vortical flow field. Near the leading edge of the stator, the leakage flow from the front partial clearance generates the tip leakage vortex, which produces loss from the leading edge to 10 percent chord position. At the mid-chord, the hub-corner separation vortex suffers a breakdown, resulting in the widespread huge loss production. It is shown from limiting streamlines on the suction surface of the stator that a reverse flow region expands radially from the solid part of the stator tip toward the downstream. From 50 percent chord position to the trailing edge of the stator, the leakage flow through the rear partial clearance interacts with the secondary flow on the hub wall. The leakage vortex generated along the rear partial clearance becomes a major loss factor there.

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